论文标题
同质代数品种和传递性程度
Homogeneous algebraic varieties and transitivity degree
论文作者
论文摘要
令$ x $为代数品种，以便集团$ \ text {aut}（x）$在$ x $ prantility上作用。我们将$ x $的传输度定义为最大数量$ m $，以使$ x $上的$ \ text {aut}（x）$的操作是$ m $ thansantive。如果$ \ text {aut}（x）$的操作是所有$ m $的$ m $传递，则通透性度无限。我们计算所有准植物曲折品种以及代数群的许多同质空间的传递性。另外，我们讨论了与此不变的猜想和开放性问题。
Let $X$ be an algebraic variety such that the group $\text{Aut}(X)$ acts on $X$ transitively. We define the transitivity degree of $X$ as a maximal number $m$ such that the action of $\text{Aut}(X)$ on $X$ is $m$-transitive. If the action of $\text{Aut}(X)$ is $m$-transitive for all $m$, the transitivity degree is infinite. We compute the transitivity degree for all quasi-affine toric varieties and for many homogeneous spaces of algebraic groups. Also we discuss a conjecture and open questions related to this invariant.
